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Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
Radiation physics 2
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Radiation physics 2

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  • 1. Physics Applied to Radiology Chapter 3 Fundamentals of Physics
  • 2. Physics
    • natural science
    • deals with matter and energy
      • defines & characterizes
      • interactions between matter and energy
  • 3. Matter
    • a physical substance
    • characteristics of all matter
      • occupies space
      • has mass
  • 4. Energy
    • capacity for doing work
  • 5. Math
    • exact vs. approximate numbers
      • exact -- defined or counted
      • approximate -- measured
    • examples
      • your height
      • # of chairs in room
      • # of seconds in a minute
      • # seconds to run 100 m dash
  • 6.
    • # of digits in a value when...
      • leading & trailing zeros are ignored
        • trailing 0 may be designated as significant
      • the decimal place is disregarded
    • How many significant figures?
        • Value: significant figures
        • 3.47
        • 0.039
        • 206.1
        • 5.90
    Significant Figures
  • 7.
    • # of digits in a value when...
      • leading & trailing zeros are ignored
        • trailing 0 may be designated as significant
      • the decimal place is disregarded
    • How many significant figures?
        • Value: significant figures
        • 3.47 3
        • 0.039 2
        • 206.1 4
        • 5.90 2
    Significant Figures
  • 8. Accuracy vs. Precision
    • accuracy -- # of significant figures
        • 3.47 is more accurate than 0.039
    • precision -- decimal position of the last significant figure
        • 0.039 is more precise than 3.47
  • 9. Example
    • Describe the accuracy and precision of the following information.
      • 2.5 cm metal sheet with a .025 cm coat of paint
        • accuracy is same for both (2 sig. fig.)
        • precision is > for paint (1/1000 vs. 1/10)
  • 10. Rounded Numbers
    • all approximate # are rounded
    • last digit of approx. number is rounded
    • last sig. fig. of an approx. # is never an accurate #
    • error of last number is ½ of the last digit's place value
      • (if place value is .1 then error = .05)
  • 11. Rounded Number
    • example:
      • if a measured value = 32.63
        • error is .005 (½ of .01)
        • actual # is between
        • 32.635 (32.63 + .005)
        • 32.625 (32.63 - .005)
  • 12. Rounding Rules
    • round at the end of the total calculation
      • do not round after each step in complex calculations
    • when - or + use least precise #
      • (same # of decimal places)
    • when x or ÷ use least accurate #
      • (same # of sig. figures)
  • 13. Rounding Example 1
    • 73.2
    • 8.0627
    • 93.57
    • + 66.296
    • 241.1287
    • 241.1 # decimal places = to least precise value
  • 14. Rounding Example 2
    • 2.4832
    • x 30.51
    • 75.762432
    • 75.76 # significant figures = to least accurate number
  • 15. Numerical Relationships
    • direct linear
      • as x  y  (or vice versa)
      • example formula y = k x
      • expressed as proportion y  x
      • example: x y (for y = 5x)
      • 1 5
      • 2 10
      • 3 15
  • 16. Numerical Relationships
    • direct exponential
      • direct square (or other exponent)
      • as x  y  by an exponential value  (or vice versa)
      • example formula y = k x 2
      • expressed as proportion y  x 2
      • example: x y (for y = 5x 2 )
      • 1 5
      • 2 20
      • 3 45
  • 17. Numerical Relationships (cont.)
    • indirect
      • as x  y 
      • example formula x y = constant
      • expressed as proportion y  1/x
      • example: x y (for xy = 100)
      • 1 100
      • 2 50
      • 4 25
  • 18. Numerical Relationships (cont.)
    • indirect exponential
      • inverse square (or other exponent)
      • as x  y  by an exponential value  (or vice versa)
      • example formula y x 2 = constant
      • expressed as proportion y  1/ x 2
      • example: x y (for x 2 y = 100)
      • 1 100
      • 2 25
      • 4 6.25
  • 19. Graphs
    • used to display relationships between 2 variables
      • Y-axis (dependent) measured value
      • X-axis (independent) controlled value
    x-axis y-axis
  • 20. Graphic Relationships ( on linear graph paper)
    • slope (left to right)
      • direct = ascending
      • indirect = descending
    • shape
      • linear = straight
      • exponential = curved
  • 21. Evaluating Graphed Information
    • identify variables
    • describe shape & slope of line
    • correlate information to theory
  • 22. Example #1
      • Relationship of mA to Intensity
  • 23. Example #1 (evaluated)
      • Relationship of mA to Intensity
        • variables
          • independent = mA
          • dependent = Exposure
        • shape & slope
          • slope = ascending (=direct)
          • shape = straight line (=linear)
        • correlate to theory
          • mA has a direct linear relationship to exposure; as mA increases exposure increases in a similar fashion; the graph demonstrates that if you double the mA (200 to 400) you also double the exposure (30 mR to 60 mR )
  • 24. Example #2
    • Relationship of the # days before exam to amount of study time
  • 25. Quantities & Units
    • quantity = measurable property
      • quantity definition (what is measured)
      • length distance between two points
      • mass amount of matter (not weight)
      • time duration of an event
    • unit = standard used to express a measurement
      • quantity unit other units
      • length meter
      • mass kilogram
      • time second
  • 26. Unit Systems
    • System length mass time
    • English foot slug (pound) second
    • metric SI** meter kilogram second
      • ** also ampere, Kelvin, mole, candela
    • metric MKS meter kilogram second
    • metric CGS centimeter gram second
    • Do not mix unit systems when doing calculations!!
  • 27. Converting Units
    • convert 3825 seconds to hours
      • identify conversion factor(s) needed
      • factors needed: 60 sec = 1 min & 60 min = 1 hour
      • arrange factors in logical progression
        • For seconds  hours
        • sec  min/sec  hour/min
      • set up calculation
  • 28. Dimensional Prefixes Bushong, table 2-3 (pg 23)
    • used with metric unit systems
    • modifiers used with unit
    • a power of 10 to express the magnitude
    • prefix symbol factor numerical equivalent
    • tera- T 10 12 1 000 000 000 000
    • giga- G 10 9 1 000 000 000
    • mega- M 10 6 1 000 000
    • kilo- k 10 3 1 000
    • centi- c 10 -2 .01
    • milli m 10 -3 .001
    • micro-  10 -6 .000 001
    • nano- n 10 -9 .000 000 001
    • pico- p 10 -12 .000 000 000 001
  • 29. Rules for Using Prefixes
    • To use a prefix divide by prefix value & include the prefix with the unit
    • To remove a prefix multiply by prefix value & delete prefix notation from the unit
  • 30. Base Quantities & Units (SI)
    • describes a fundamental property of matter
    • cannot be broken down further
    • quantity SI unit definition for quantity
    • length meter distance between two points
    • mass kilogram amount of matter (not weight)
    • time second duration of an event
  • 31. Derived Quantities & Units
    • properties which arrived at by combining base quantities
    • quantity units definition for quantity
    • area m x m m 2 surface measure
    • volume m x m x m m 3 capacity
    • velocity m/s m/s distance traveled per unit time
    • acceleration m/s/s m/s 2 rate of change of velocity
    • ms -2
  • 32. Derived Quantities with Named Units
    • quantities with complex SI units
    • quantity units definition
    • frequency Hertz Hz # of ?? per second
    • force Newton N "push or pull"
    • energy Joule J ability to do work
    • absorbed dose Gray Gy radiation energy deposited (rad) in matter
  • 33. Solving Problems
    • 1. Determine unknown quantity
    • 2. Identify known quantities
    • 3. Select an equation (fits known & unknown quantities)
    • 4. Set up numerical values in equation
      • same unit or unit system
    • 5. Solve for the unknown
      • write answer with magnitude & units
      • raw answer vs. answer in significant figures
  • 34. Mechanics
    • study of motion & forces
    • motion = change in position or orientation
    • types of motion
      • translation
        • one place to another
      • rotation
        • around axis of object's mass
  • 35. Measuring Quantities in Mechanics
    • all have magnitude & unit
    • scalar vs. vector quantities
      • Scalar -- magnitude & unit
      • Vector -- magnitude, unit & direction
    run 2 km vs run 2 km east
  • 36. Vector Addition/Subtraction
    • requires use of graphs, trigonometry or special mathematical rules to solve
    • example:
    F 1 F 2 F 1 + F 2 = Net force
  • 37. Quantities in Mechanics
    • speed
      • rate at which an object covers distance
        • rate
          • indicates a relationship between 2 quantities
          • $/hour exams/tech # of people/sq. mile
      • speed = distance/time
      • speed is a scalar quantity
  • 38. Speed (cont.) d in m t in s v = m/s same at all times total distance total time General Formula: Variations: instantaneous uniform average v at 1 point in time v = d t distance time
  • 39. Speed Example
    • An e - travels the 6.0 cm distance between the anode & the cathode in .25 ns. What is the e - speed? [Assume 0 in 6.0 is significant]
      • v = ?? 6.0 cm = distance .25 ns = time
      • v = d / t (units: m /s  need to convert)
      • 6.0 cm = 6.0 x 10 -2 m .25 ns = .25x10 -9 s
      • = 6 x 10 -2 m / .25x10 -9 s
      • = 2.40000 x 10 8 m/s (raw answer)
      • = 2.4 x 10 8 m/s (sig. fig. answer)
  • 40. Velocity
    • speed + the direction of the motion
    • vector quantity
      • A boat is traveling east at 15 km/hr and must pass through a current that is moving northeast at 10 km/hr . What will be the true velocity of the boat?
  • 41. Acceleration
    • rate of change of velocity with time
      • if velocity changes there is acceleration
    • includes:  v  v  direction
    • formula:
     v = v f - v i units v in m/s t in s a = m/s 2 a =  v  t
  • 42. Acceleration Example
    • A car is traveling at 48 m/s. After 12 seconds it is traveling at 32 m/s. What is the car’s acceleration?
      • a = ? 48 m/s = v i 12 s =  t 32 m/s = v f
      • a =  v /  t
      •    v = v f - v i = 32m/s - 48 m/s = -16 m/s
      • a = -16m/s / 12 s = -1.3333333333 m/s 2
      • = -1.3 m/s 2 [ -sign designates slowing down]
  • 43. Application of v and a in Radiology
    • KE (motion) of e- used to produce x rays
      • controlling the v of e- enables the control of the photon energies
    • Brems photons are produced when e - undergo a -a close to the nucleus of an atom
  • 44. Newton's Laws of Motion
    • 1. Inertia
    • 2. Force
    • 3. Recoil
  • 45. Newton's First Law
    • defined -- in notes
    • inertia: resistance to a  in motion
      • property of all matter
      • mass = a measure of inertia
  • 46. Inertia
    • Semi-trailer truck
      • large mass
      • large inertia
    • Bicycle
      • small mass
      • small inertia
  • 47. Newton's 2nd Law (Force)
    • Force
      • anything that can  object's motion
      • Fundamental forces
        • Nuclear forces
          • "strong" & "weak"
        • Gravitational force
        • Electromagnetic force
  • 48. Mechanical Force
    • push or pull
    • vector quantity
      • net force = vector sum of all forces
      • push on box + friction from floor
    • equilibrium -- net force = 0
    Vector sum
  • 49. 2nd Law (Force)
    • defined -- in notes
    • formula for the quantity “force”
      • force = mass x acceleration
      • F = m x a
    Newton N a =  v  t kg m s 2
    • units kg x m/s 2
  • 50. Example Problem for 2nd Law
    • What is the net force needed to accelerate a 5.1 kg laundry cart to 3.2 m/s 2 ?
      • F =?? 5.1 kg = mass 3.2 m/s 2 = acceleration
      • F = m a
      • = 5.1 kg x 3.2 m/s 2
      • = 16.32 kg m/s 2
      • = 16 N
  • 51. Example 2:
    • A net force of 275 N is applied to a 110 kilogram mobile unit. What is the unit's acceleration?
      • acceleration =?? 275 N = F 110 kg = mass
      • F = m a
      • a = F / m
      • = 275[kg m/s 2 ] / 110kg
      • = 2.5 m/s 2
  • 52. Example 3
    • An object experiences a net force of 376N. After 2 seconds the change in the object's velocity 15m/s. What is the object's mass?
    • mass =?? 376 N = F 2 s =  t 15 m/s =  v
      • F = m a  m = F / a
      • a =  v/  t
      • = 15 m / s / 2 s = 7.5 m/s 2
      • m = 376 [kg m/s 2 ] / 7.5 m/s 2
      • = 50.13333333333 kg = 50 kg
  • 53. Weight
    • adaptation of Newton's 2nd law
    • weight = force caused by the pull of gravitation
      • weight  mass
      • gravitational force inertia of the object
      • varies with gravity always constant
      • unit = N [pound] unit = kg [slug]
    • when g is a constant then weight proportional mass
  • 54. Weight (cont.)
    • formula for quantity “weight”
    • modified from force formula
      • F = m x a
      • Wt. = m x g g earth = 9.8m/s 2
    Newton N kg m s 2 units kg x m/s 2
  • 55. Weight Problem
    • What is the weight (on earth) of a 42 kg person?
      • Wt. = ?? 42 kg = mass [9.8m/s 2 = gravity]
      • Wt. = m x g
      • = 42 kg x 9.8m/s 2
      • = 411.6 kg m/ s 2
      • = 410 N
  • 56. Weight Problem #2
    • What is the mass of a 2287N mobile x-ray unit?
      • mass = ?? 2287N = Wt [9.8m/s 2 = gravity]
      • Wt. = m x g
      • m = Wt. / g
      • = 2287N / 9.8m/s 2
      • = 233.3673469388 kg
      • = 233.4 kg
  • 57. 3rd Law (Recoil)
    • Defined -- in notes
      • no single force in nature
      • all forces act in pairs
        • action vs. reaction
    • formula
      • F AB = -F BA
    A B
  • 58. Momentum (Linear)
    • measures the amount of motion of an object
    • tendency of an object to go in straight line when at a constant velocity
    • formula
      • p = m x v
    • units
      • = kg x m/s
      • =
    kg m s
  • 59. Momentum vs. Mass (Inertia)
    • p = m x v
    • p  m
    Direct proportional relationship  m =  p  m =  p
  • 60. Momentum vs. Velocity
    • p = m x v
    • p  v
    Direct proportional relationship 50 km/hr  v =  p 100 km/hr  v =  p
  • 61. Momentum Problem
    • What is the momentum of a 8.8 kg cart that has a speed of 1.24 m/s?
      • p = ?? 8.8 kg = mass 1.24 m/s = velocity
      • p = m x v
      • = 8.8 kg x 1.24 m/s
      • = 10.912 kg m/s
      • = 11 kg m/s
  • 62. Momentum Problem #2
    • What is the speed of a 3.5x10 4 kg car that has a momentum of 1.4x10 5 kg m/s?
      • velocity = ?? 3.5x10 4 kg = mass 1.4x10 5 kg m/s = momentum
      • p = m x v
      • v = p / m
      • = 1.4x10 5 kg m/s / 3.5x10 4 kg
      • = 4.0 x 10 0 m/s
      • = 4.0 m/s
  • 63. Conservation Laws
    • Statements about quantities which remain the same under specified conditions.
    • Most Notable Conservation Laws
      • Conservation of Energy
      • Conservation of Matter
      • Conservation of Linear Momentum
  • 64. Conservation of Linear Momentum
    • momentum after a collision will equal momentum before collision
    • results in a redistribution momentum among the objects
    • p 1 = p 2
    • m 1 v 1 = m 2 v 2
  • 65. Example before collision collision occurs after collision m 1 v 1 = 1 kg m/s mv = 0 mv = 0 m 2 v 2 = 1 kg m/s
  • 66. Example #2 m 1 v 1 = 5 kg m/s mv = 0 m 2 v 2 = 5 kg m/s before collision collision occurs after collision m 2 = m A + m B v 2 = v A + v B A B A B
  • 67. Work
    • defined -- in notes
      • measures the change a force has on an object's position or motion
      • If there is NO change in position or motion, NO mechanical work is done.
    F d
  • 68. Work (cont.)
    • formula
      • Work = force x distance
      • W = F x d
    • units = N x m
      • =
    kg m s 2 x m kg m 2 s 2 = Joule J =
  • 69. Example
    • How much mechanical work is done to lift a 12 kg mass 8.2 m off of the floor if a force of 130 N is applied?
    • work = ?? 12 kg = mass 8.2 m = distance 130 N = force
      • W = F x d
      • = 130 N x 8.2 m
      • = 1066 N m
      • = 1100 J (1.1 kJ)
  • 70. Example #2
    • A 162 N force is used to move a 45 kg box 32 m. What is the work that is done moving the box?
      • work = ?? 162 N = force 45 kg = mass 32 m = distance
      • W = F x d
      • = 162 N x 32 m
      • = 5184 N m
      • = 5200 J or 5.2 kJ
  • 71. Energy
    • property of matter
    • enables matter to perform work
    • broad categories
      • Kinetic Energy: due to motion
      • Potential Energy: due to position in a force field
      • Rest Energy: due to mass
  • 72. Kinetic Energy
    • work done by the motion of an object
      • translation, rotation, or vibration
    • formula
      • KE = ½ mass x velocity squared
      • = ½ m v 2
    • units = kg x [m/s] 2
    kg m 2 s 2 = Joule J =
  • 73. Example
    • Find the kinetic energy of a 450 kg mobile unit moving at 6 m/s.
      • kinetic energy = ?? 450 kg = mass 6 m/s = velocity
      • KE = ½ m v 2
      • = ½ x 450 kg x [6 m/s] 2
      • = 8100 kg m 2 /s 2
      • = 8000 J or 8 kJ
  • 74. Potential Energy
    • capacity to do work because of the object's position in a force field
    • fields
      • nuclear
      • electromagnetic
      • gravitational
  • 75. Gravitational Potential Energy
    • barbell with PE
    • formula
      • PE g = mass x gravity x height
      • = m x g x h
    • units
      • = kg x m/s 2 x m
      • =
    h g m = Joule J kg m 2 s 2
  • 76. Example
    • How much energy does a 460 kg mobile unit possess when it is stationed on the 3rd floor of the hospital? (42m above ground)
    • PE = ?? 460 kg = mass 42 m = height [9.8 m/s 2 = gravity]
      • Pe g = m x g x h
      • = 460 kg x 9.8 m/s 2 x 42 m
      • = 189 336 kg m 2 /s 2
      • = 190 000 J or 1.9x10 5 J or 190 kJ
  • 77. Rest Mass Energy
    • energy due to mass
    • Einstein's Theory
    • formula (variation of KE formula)
      • E m = mass x speed of light squared
      • = m c 2 [ c = 3x10 8 m/s ]
    • units = kg x [m/s] 2
    kg m 2 s 2 = Joule J =
  • 78. Example
    • What is the energy equivalent of a 2.2 kg object?
    • E m = ?? 2.2 kg = mass [3x10 8 m/s = speed of light]
      • E m = m c 2
      • = 2.2 kg x [3x10 8 m/s ] 2
      • = 1.98 x 10 17 kg m 2 /s 2
      • = 2.0 x 10 17 J [trailing 0 is significant]
  • 79. Conservation Of Energy (Matter)
    • Energy is neither created nor destroyed but can be interchanged
    • (Matter is neither created nor destroyed but can be interchanged)
    • Because mass has rest energy, conservation of matter & energy can be combined
  • 80. Power
    • Rate at which work is done
      • Faster work = more power
    • Rate at which energy changes
      • Large E  = more power
  • 81. Power (cont.)
    • formula
      • power = work / time or  energy / time
      • P = W / t or  E / t
    • units = J / s
    kg m 2 s 3 = Watt W = kg m 2 s 2 = s
  • 82. Example
    • How much power is used when an 80N force moves a box 15 m during a 12 s period of time?
      • (hint: solve for work first)
      • P = ?? 80 N = force 15 m = distance 12 s = time
      • P = W / t & W = F d
      • P = ( F d ) / t
      • = ( 80 N x 15 m ) / 12 s
      • = 100 Nm/s
      • = 100 W
  • 83. Heat energy
    • internal kinetic energy of matter
      • from the random motion of molecules or atoms
      • KE & PE of molecules
      • heat E in matter moves from area of higher E in object to area of lower internal E
    • Unit -- Calorie (a form of the joule)
      • amount of heat required to raise one gram of water one degree Celsius.
  • 84. Heat Transfer
    • movement of heat energy from the hotter to cooler object (or portion of object)
    • 3 methods of transfer
      • conduction
      • convection
      • radiation
  • 85. conduction
    • primary means in solid objects
    • classification of matter by heat transfer
      • conductors--rapid transfer
      • insulator--very slow to transfer
  • 86. convection
    • primary means in gasses and liquids
    • convection current--continuing rise of heated g/l and sinking of cool g/l
  • 87. radiation
    • transfer without the use of a medium
      • (i.e. no solid, liquid or gas)
    • occurs in a vacuum
  • 88. Heat Radiation
    • term “radiation” may simply refer to heat energy and not the transfer of heat
    • infra-red radiation, part of EM spectrum, is heat energy
  • 89. Effects of Heat Transfer
    • change in physical state of matter
      • solid  liquid  gas
      • melt boil
    • change in temperature
      • measure of the average KE of an object
      • relative measure of sensible heat or cold
  • 90. Temperature Scales
      • Scales Boil (steam) Freeze (ice) No KE
      • Fahrenheit 212° 32° -460°
      • Celsius 100° 0° -273°
      • Kelvin (SI) 373 273 0
      • 1K = 1°C = 1.8°F
      • Conversion formulae
      • °F = 32 + (1.8 °C)
      • °C = (°F - 32)  1.8
      • K = °C + 273

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